# Common Core: High School - Geometry : Drawing Transformed Figures: CCSS.Math.Content.HSG-CO.A.5

## Example Questions

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### Example Question #1 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

If a triangle is in quadrant three and undergoes a transformation that moves each of its coordinate points to the left three units and down one unit, what transformation has occurred?

Extension

Translation

Reflection

Rotation

Translation

Explanation:

To determine the type of transformation that is occurring in this particular situation, first recall the different types of transformations.

Translation: To move an object from its original position a certain distance without changing the object in any other way.

Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.

Reflection: To flip the orientation of an object over a specific line or function.

Rotation: To rotate an object either clockwise or counter clockwise around a center point.

Since each of the triangle's coordinates is moved to the left and down, it is seen that the size and shape of the triangle remains the same but its location is different. Therefore, the transformation the triangle has undergone is a translation.

### Example Question #2 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

If a rectangle has the coordinate values, , and  and after a transformation results in the coordinates , and  identify the transformation.

Non of the others

Dilation

Rotations

Reflection

Extension

Reflection

Explanation:

"If a rectangle has the coordinate values, , and  and after a transformation results in the coordinates  , and  identify the transformation."

A transformation that changes the  values by multiplying them by negative one is known as a reflection across the -axis or the line

Therefore, this particular rectangle is being reflected across the -axis because the opposite of all the  values have been taken.

### Example Question #3 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

If a rectangle has the coordinate values, , , , and  and after a transformation results in the coordinates , , , and  identify the transformation.

Extension

Reflection

Rotation

Dilation

Reflection

Explanation:

"If a rectangle has the coordinate values, , and  and after a transformation results in the coordinates , and  identify the transformation."

A transformation that changes the  values by multiplying them by negative one is known as a reflection across the -axis or the line

Therefore, this particular rectangle is being reflected across the -axis because the opposite of all the  values have been taken.

### Example Question #4 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

If a rectangle has the coordinate values, , and  and after a transformation results in the coordinates , and  identify the transformation.

Reflection

Translation

Dilation

Rotation

Translation

Explanation:

To identify the transformation that is occurring in this particular problem, recall the different transformations.

Translation: To move an object from its original position a certain distance without changing the object in any other way.

Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.

Reflection: To flip the orientation of an object over a specific line or function.

Rotation: To rotate an object either clockwise or counter clockwise around a center point.

Looking at the starting and ending coordinates of the rectangle,

, and   to  , and

Since all the  coordinates are increasing by two this is known as a translation.

### Example Question #5 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a trapezoid are, , , , and . What are the coordinates of this trapezoid after it is reflected across the -axis?

Explanation:

To find the reflected image of the trapezoid, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the horizontal axis on the coordinate grid and is equivalent to the line .

Plot the points of the original trapezoid on the coordinate grid.

From here, to reflect the image across the -axis take the negative of all the  values.

This change results in the following,

Therefore, the coordinates of the reflected trapezoid are

### Example Question #6 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a trapezoid are, , , , and . What are the coordinates of this trapezoid after it is reflected across the -axis?

Explanation:

To find the reflected image of the trapezoid, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the vertical axis on the coordinate grid and is equivalent to the line .

Plot the points of the original trapezoid on the coordinate grid.

From here, to reflect the image across the -axis take the opposite of all the  values.

This change results in the following,

Therefore, the coordinates of the reflected trapezoid are

### Example Question #7 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a trapezoid are, , , , and . What are the coordinates of this trapezoid after it is reflected across the  and -axis?

Explanation:

To find the reflected image of the trapezoid, first identify how it is being reflected. This particular problem states that it is being reflected over the  and -axis. This means the reflected image will be in the fourth quadrant.

Plot the points of the original trapezoid on the coordinate grid.

From here, to reflect the image across the line both axis take the opposite of all the coordinate values.

This change results in the following,

Therefore, the coordinates of the reflected trapezoid are

### Example Question #8 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a trapezoid are, , , and . What are the coordinates of this trapezoid after it is reflected across the -axis?

Explanation:

To find the reflected image of the triangle, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the vertical axis on the coordinate grid and is equivalent to the line .

Plot the points of the original triangle on the coordinate grid.

From here, to reflect the image across the -axis take the negative of all the  values.

This change results in the following,

Therefore, the reflected triangle has coordinates at

### Example Question #9 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a trapezoid are, , , and . What are the coordinates of this triangle after it is reflected across the  and -axis?

Explanation:

To find the reflected image of the triangle, first identify how it is being reflected. This particular problem states that it is being reflected over the  and -axis. This means the reflected image will be in the fourth quadrant.

Plot the points of the original trapezoid on the coordinate grid.

From here, to reflect the image across the line both axis take the opposite of all the coordinate values.

This change results in the following,

Therefore, the coordinates of the reflected triangle are

### Example Question #10 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a triangle are, , , and . What are the coordinates of this triangle after it is reflected across the -axis?

Explanation:

To find the reflected image of the triangle, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the horizontal axis on the coordinate grid and is equivalent to the line .

Plot the points of the original triangle on the coordinate grid.

From here, to reflect the image across the -axis take the negative of all the  values.

This change results in the following,

Therefore, the reflected triangle has coordinates at

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